
where \(P_{\mu \nu \rho \sigma }=\dfrac{\partial \mathcal {L}}{\partial R^{\mu \nu \rho \sigma }}\)  and \(\mathcal {R}_{\mu \nu }=P_\mu \,^{\alpha \beta \gamma }R_{\nu \alpha \beta \gamma }\)[1]}. Derived from an action, the tensor \(\varepsilon _{\mu \nu }\)  is symmetric and divergence-free. Therefore; it can be coupled to an energy-momentum tensor as \(\varepsilon _{\mu \nu } \propto T_{\mu \nu }\) , yielding a generalization of Einstein's equations. However, the last term in () contains derivatives of the metric tensor of order higher than two, which in general spoils the unitarity of the energy. Demanding second-order field equations \((\nabla _\alpha P^{\alpha \mu \nu \beta }=0)\)  gives a very special class of theories [2]}, Lovelock gravitysee Section 15.4 of [3]} for a pedagogical exposition. [4]}, [5]}, [6]}, that possesses a unitary massless spin-2 excitation around any of its constant curvature vacua [7]}. The Lagrangian of Lovelock gravity is given by
\(\mathcal {L}=\sum _{m} c_m \mathcal {L}_m,\) 
